There is a long line of work which focuses on constructing coresets for subspace approximation with sum of squared distances loss function, as well as for the \(k\) -means problem (see, e.g., [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}). [5]} give the first coresets of size independent of \(d\) . For subspace approximation, they give strong coresets of size \(O(k/\epsilon )\) , and \(\widetilde{O}(k^3/\epsilon ^4)\)  for \(k\) -means. [17]} improve the result and give an input sparsity time algorithm to construct the coreset.
